Generating sets that pass is straightforward: here's code that generates full sets for a given prime, and you can mask out a subset of the values with undef. All such sets should return true when queried with the same prime:

#!/usr/bin/perl
use strict;
use warnings;

my($prime, $range, $count) = @ARGV;

for (1 .. $count) {
    # report the full range for a random start point
    my $start = int rand(2 ** 32 - $range);
    print join(' ', map val($start + $_), 0 .. $range - 1), "\n";
}
exit 0;

# return the $p-adic order of $n
sub val {
    my($n) = @_;
    my $val = 0;
    ++$val, $n /= $prime while 0 == $n % $prime;
    return $val;
}

[download]

It's less obvious how to generate a useful collection of sets that should not pass. Best I can suggest is to take one of the passing sets, randomly increment or decrement an element (that has not been masked out), and see if the valid_set() function in my original post rejects it.

In reply to Re^4: checking a set of numbers for consistency mod p by hv
in thread checking a set of numbers for consistency mod p by hv

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